The natural evolution of tuberculosis in the absence of any medical interventions and its evolution in populations where control measures are implemented, are studied using various mathematical techniques and especially those of stochastic models. In developed countries the numbers of tuberculosis cases increased and then declined, even before the introduction of effective therapy. Although now curable, tuberculosis remains endemic in developing countries and among infectious diseases it is the leading cause of death worldwide. Serious questions have been raised with respect to the efficacy of the control measures currently available and the reasons for their failure to control the spread of tuberculosis in some areas. This thesis investigates the spread of tuberculosis in the absence and in the presence of medical interventions and addresses questions about the endemicity of the disease and the efficacy of the controls, via stochastic models describing the dynamics of the infection. In particular, the probability of extinction of the disease, the time until extinction, the size of an individual epidemic, and the distributions of the numbers of infected and infectious individuals are considered. Special attention is given to epidemiological indices, such as prevalence, risk of infection, incidence, and mortality, which are used by public health authorities to assess the severity of an epidemic. Approximating methods, including the use of deterministic models, are investigated and their results are compared with those from numerical simulations of the stochastic models being studied. The effect of chemotherapy in controlling an epidemic is assessed by the percentage reduction in the epidemiological indices for various levels of detection and cure rates. The effect of BCG vaccination is studied separately for various coverage and protective levels
